Using Pythagoras, probably.
Lay the triangle on its side and draw the perpendicular height you're supposed to find. Then you got 2 right angle triangles.
Let h be the perp height and c = a+b be the length of the base (where a and b are the lengths to the perpendicular h.
Then you have two equations where are the lengths of the sloping sides.
Can you draw it? I can't be bothered myself, it's too much like hard work for me.